Problem: Find the slope and y-intercept of the line that is ${\text{parallel}}$ to $\enspace {y = -3x - 3}\enspace$ and passes through the point ${(3, -4)}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$
Parallel lines have the same slope. The slope of the blue line is ${-3}$ , so the equation of our parallel line will be of the form $\enspace {y = -3x + b}\enspace$ We can plug our point, $(3, -4)$ , into this equation to solve for ${b}$ , the y-intercept. $-4 = {-3}(3) + {b}$ $-4 = -9 + {b}$ $-4 + 9 = {b} = 5$ The equation of the parallel line is $\enspace {y = -3x + 5}\enspace$. ${m = -3, \enspace b = 5}$